Answer:
y = 4x + 31
Step-by-step explanation:
We are given that a line contains the point (-9,-5).
We also know that this line is parallel to the line that has the equation y = 4x + 3.
We want to write the equation of the unknown line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept.
Parallel lines have the same slopes.
The equation y = 4x + 3 is written in slope-intercept form. Therefore, the slope of the line is 4, as 4 is in the place of where m (the slope) is.
It is also the slope of the line we want to write.
Since we now know the slope of the line, we can substitute that value into the equation.
Replace m with 4 in y=mx+b.
y = 4x + b
Now we need to find b.
As the equation passes through the point (-9, -5), we can use its values to help solve for b.
Substitute -9 as x and -5 as y.
-5 = 4(-9) + b
Multiply
-5 = -36 + b
Add 36 to both sides.
31 = b
Substitute 31 as b in the equation.
y = 4x + 31
Topic: parallel and perpendicular lines.
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