Answer:
y = 4/5x + 3/5
Step-by-step explanation:
In the slope-intercept form, y = mx + b, we need to find the values of the slope (m) and the y-intercept.
Using points (-7, -5) and (3, 3), we can calculate for the slope of the equation given the formula:
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Let (x1, y1) = (-7, -5)
and (x2, y2) = (3, 3).
Plug the given values into the slope formula:
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{3 - (-5)}{3 - (-7)} = \frac{3 + 5}{3 + 7} = \frac{8}{10} = \frac{4}{5}[/tex]
Therefore, the slope of the line is 4/5.
Next, we need to find out the value of the y-intercept (b).
We can use one of the given points, (3, 3), along with the slope (4/5) to solve for the y-intercept:
y = mx + b
3 = 4/5(3) + b
3 = 12/5 + b
Subtract 12/5 from both sides:
3 - 12/5 = 12/5 - 12/5 + b
3/5 (or 0.6) = b
Therefore, the y-intercept is 3/5.
We can now establish our linear equation as:
y = 4/5x + 3/5
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