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.

necessaryh 2020-11-05 Answered
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.

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Expert Answer

casincal
Answered 2020-11-06 Author has 9889 answers

(a) y-intercept and slope: In a linear equation \(y=b_0+b_1x\), the constant \(b1\) be the slope and \(b_0\) 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_1) 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 > 0, the slope of the linear equation \(\displaystyle{y}={b}_{{0}}+{b}_{{1}}{x}\) is downward if \(\displaystyle{b}_{{1}}{<}{0}\), 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 \(\displaystyle{\left({x}_{{2}},{y}_{{2}}\right)}={\left({4},{0}\right)}\)
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