Question

Please help! I will mark as brainliest IF answer is right. <3

Answer 1

Answer:

$y=\frac{7}{4}x-9$

Step-by-step explanation:

Question:

Find the equation of the line through the point (4, -2) with slope $\frac{7}{4}$

Answer + Step-by-step explanation:

Answer: $y=\frac{7}{4}x-9$

Step-by-step explanation:

When trying to find the equation of a line passing through a point and then given the slope, always remember if you're trying to write the equation in slope-intercept form, find the slope and the y-intercept of the equation.

Slope-Intercept form: y = mx + b where m = slope and b = y-intercept

so the slope is already given but we have to find the y-intercept.

so... the equation of the line with a slope of $\frac{7}{4}$ is:

$y=\frac{7}{4}x$

but in addition, we need a y-intercept so...

$y=\frac{7}{4}x+b$

now use the given point on the question "(4, -2)" to solve for the y-intercept

so plug in the coordinates of the point in the equation:

$y=\frac{7}{4}x+b$

$(-2)=\frac{7}{4}(4)+b$

$-2=\frac{28}{4} +b$

$-2=7+b$

$b=-2-7$

$b=-9$

so the y-intercept of the line is -9

and the equation of the line is $y=\frac{7}{4}x-9$