Given linear equation y = 0.5x – 2 a. find the y-intercept and slope. b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation. c. use two points to graph the equation.

Given linear equation y = 0.5x – 2 a. find the y-intercept and slope. b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation. c. use two points to graph the equation.

Question
Linear equations and graphs
asked 2020-11-05
Given linear equation y = 0.5x – 2
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.

Answers (1)

2020-11-06
(a) y-intercept and slope: In a linear equation y=b_0+b_1xZSK, the constant b1 be the slope and b0 be the y-intercept form and x is the independent variable and y is the dependent variable. Comparing the given equation with the general form of linear equation the slope of the equation is 0.5 and the y-intercept is –2. Therefore, the y-intercept is –2 and the slope of the linear equation (b_1ZSK) is 0.5. (b) It is known that, the slope of the linear equation \(\displaystyle{y}={b}_{{0}}+{b}_{{1}}{x}\) is upward if b_1 > 0ZSK, the slope of the linear equation \(\displaystyle{y}={b}_{{0}}+{b}_{{1}}{x}\) is downward if \(\displaystyle{b}_{{1}}{<}{0}\)</span>, and the slope of the linear equation \(\displaystyle{y}={b}_{{0}}+{b}_{{1}}{x}\) is horizontal if \(\displaystyle{b}_{{1}}={0}\) .
Thus, in the given equation \(\displaystyle{y}={0.5}{x}–{2},{b}_{{1}}\) is 0.5, which is greater than 0.
Thus, the slope is upward.
(c) Graph by using two points:
The two points \(\displaystyle{\left({x}_{{1}},{y}_{{1}}\right)}{\quad\text{and}\quad}{\left({x}_{{2}},{y}_{{2}}\right)}\) on the given line are obtained as follows:
If x=0
\(\displaystyle{y}={\left({0},{5}\times{0}\right)}-{2}\)
y=-2
Thus, one point on the line is \(\displaystyle{\left({x}_{{1}},{y}_{{1}}\right)}={\left({0},-{2}\right)}\)
If x=4,
\(\displaystyle{y}={\left({0.5}\times{4}\right)}-{2}\)
y=0
Thus, the second point on the line is \(\displaystyle{\left({x}_{{2}},{y}_{{2}}\right)}={\left({4},{0}\right)}\)
image
0

Relevant Questions

asked 2020-11-29
Given linear equation y = 1.5x
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
asked 2020-11-05
Given linear equation y = -0.75x-5
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
asked 2021-01-19
Given linear equation y = -1+2x
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
asked 2020-11-02
Given linear equation y = 3+4x
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
asked 2021-01-04
Given linear equation y = 6 − 7x
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
asked 2020-12-21
Given linear equation y = -8-4x
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
asked 2020-12-06
Given linear equation y = -3x
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
asked 2021-02-25
Given linear equation y = -3
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c.use two points to graph the equation
asked 2021-02-12
We give linear equations. For each equation,
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
y=-3
asked 2021-05-14
For the equation (-1,2), \(y= \frac{1}{2}x - 3\), write an equation in slope intercept form for the line that passes through the given point and is parallel to the graph of the given equation.
...