Question

Slope = - 3/2; passes through (-4, 7)

Answer 1

`y=-(3)/(2)x+1`

Explanation:

The equation of a line in slope-intercept form is:

`y=mx+b`

Each variable represents:

"y" - y coordinate for any point on the line

"m" - slope of the line

"x" - x coordinate for any point on the line

"b" - y-intercept of the line (where the line intercepts the y-axis)

Given:

Slope = -3/2

Passes through (-4, 7) --> x = -4, y=7

Find:

y-intercept

Let's substitute the given information into the equation:

`y=mx+b\\7=-(3)/(2)(-4)+b\\7=-(-12)/(2)+b\\7=-(-6)+b\\7=6+b\\$Subtract 6 from both sides\\$b=1`

Therefore the final equation is:

`y=-(3)/(2)x+1`