Write an equation of the line passing through (-2, 5) and parallel to the line w

Emily-Jane Bray

Emily-Jane Bray

Answered question

2021-09-25

Write an equation of the line passing through (-2, 5) and parallel to the line whose equation is y = 3x + 1. Express the equation in point-slope form and slope-intercept form.

Answer & Explanation

Velsenw

Velsenw

Skilled2021-09-26Added 91 answers

Step 1
We have to write the equation of line which is passing through the point (−2,5) and parallel to the line y=3x+1.
We know that any straight line which is passing through the point (x1,y1) and slope is m then equation of line would be:
(yy1)=m(xx1)
According to question,
x1=2,y1=5
slope will be calculated from the line y=3x+1
since line is parallel hence slope will be equal
therefore, m=3 (since in equation y=mx+c, m is slope)
Step 2
Putting above values in the equation, we get
(yy1)=m(xx1)
(y-5)=3(x-(-2))
(y-5)=3(x+2)
y-5=3x+6
y=3x+6+5
y=3x+11
Hence, equation of straight line in point slope form is (y−5)=3(x+2) and in slope-intercept form is y=3x+11.
xleb123

xleb123

Skilled2023-06-15Added 181 answers

Step 1: Find the slope of the given line.
The given line has an equation of the form y=mx+b, where m represents the slope. By comparing the equation with the standard slope-intercept form, we can see that the slope of the given line is 3.
Step 2: Since the line we want to find is parallel to the given line, it will also have a slope of 3.
Step 3: Use the point-slope form of a line to write the equation.
The point-slope form of a line is given by the equation yy1=m(xx1), where (x1,y1) represents a point on the line and m is the slope.
Using the point (2,5) and the slope m=3, we can substitute these values into the point-slope form to obtain the equation:
y5=3(x(2))
Simplifying this equation gives:
y5=3(x+2)
Step 4: Convert the equation to slope-intercept form.
The slope-intercept form of a line is given by the equation y=mx+b, where m represents the slope and b represents the y-intercept.
Let's simplify the point-slope form equation to slope-intercept form:
y5=3x+6
y=3x+6+5
y=3x+11
Therefore, the equation of the line passing through the point (2,5) and parallel to the line y=3x+1 is expressed in point-slope form as y5=3(x+2) and in slope-intercept form as y=3x+11.
fudzisako

fudzisako

Skilled2023-06-15Added 105 answers

Given:
Point A: (-2, 5)
Equation of the line: y=3x+1
We know that the slope of the given line is 3. So, the line we're looking for will also have a slope of 3.
The point-slope form of a linear equation is given by yy1=m(xx1), where (x₁, y₁) represents a point on the line and m represents the slope.
Using the point A (-2, 5) and the slope m = 3, we can write the equation in point-slope form:
y5=3(x(2))
Simplifying the equation, we have:
y5=3(x+2)
Expanding the right side:
y5=3x+6
Now, let's rearrange the equation into the slope-intercept form, which is of the form y=mx+b, where m is the slope and b is the y-intercept.
y=3x+6+5
y=3x+11
Therefore, the equation of the line passing through (-2, 5) and parallel to the line y = 3x + 1 is:
Point-slope form: y5=3(x+2)
Slope-intercept form: y=3x+11
Andre BalkonE

Andre BalkonE

Skilled2023-06-15Added 110 answers

Step 1:
To find the equation of a line parallel to the line y=3x+1 and passing through the point (2,5), we need to determine the slope of the parallel line. Since parallel lines have the same slope, the slope of the parallel line will also be 3.
Using the point-slope form of a linear equation, we can write the equation as:
yy1=m(xx1) where m is the slope and (x1,y1) is the given point.
Substituting the values m=3, x1=2, and y1=5, we get:
y5=3(x(2))
Simplifying the equation:
y5=3(x+2)
Step 2:
Now, let's express the equation in slope-intercept form (y=mx+b) by simplifying further:
y5=3x+6
Adding 5 to both sides:
y=3x+6+5
Simplifying:
y=3x+11
Thus, the equation of the line passing through (2,5) and parallel to y=3x+1 is given in point-slope form as y5=3(x+2) and in slope-intercept form as y=3x+11.

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