Answer:
[tex]y=-\frac{3}{2}x+1[/tex]
Step-by-step explanation:
The equation of a line in slope-intercept form is:
[tex]y=mx+b[/tex]
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:
[tex]y=mx+b\\7=-\frac{3}{2}(-4)+b\\7=-\frac{-12}{2}+b\\7=-(-6)+b\\7=6+b\\$Subtract 6 from both sides\\$b=1[/tex]
Therefore the final equation is:
[tex]y=-\frac{3}{2}x+1[/tex]
