Answer:
[tex]y=-\frac{3}{4}x+4[/tex]
Step-by-step explanation:
Slope-intercept form: y = mx + b
Slope (m): [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Use two points on the line to find the slope (m)
(4, 1) and (-4, 7)
[tex]m=\frac{7-1}{-4-4} \\\\m=\frac{6}{-8}\\\\m=-\frac{6\div2}{-8\div2}\\\\m=-\frac{3}{4}[/tex]
y = mx + b
[tex]y=-\frac{3}{4}x+b[/tex]
Now we find b, using either (4, 1) or (-4, 7)
(4, 1)
[tex]y=-\frac{3}{4}x+b\\\\1=-\frac{3}{4}(4)+b\\\\1=-3+b\\+3 +3\\\\4=b[/tex]
[tex]y=-\frac{3}{4}x+b== > y=-\frac{3}{4}x+4[/tex]
Check your answer using either of the points:
[tex](4,1)\\y=-\frac{3}{4}x+4\\\\1=-\frac{3}{4}(4)+4\\\\1=-3+4\\\\1=1[/tex]
This statement is true
Therefore, our final answer is [tex]y=-\frac{3}{4}x+4[/tex]
Hope this helps!
