The equation of the line in slope-intercept form is: [tex]y = -\frac{3}{2}x + 8[/tex]
Recall:
Slope-intercept equation of a line is: [tex]y=mx+b[/tex]
where,
[tex]slope = m\\y-intercept = b[/tex]
We need to find the values of m and b using the graph given.
Slope (m) of the graph using two points [tex](2, 5)[/tex] and [tex](0, 8)[/tex]
[tex]Slope (m) = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Let,
[tex](2,5) = (x_1, y_1)\\(0,8) = (x_2, y_2)[/tex]
Plug in the values:
[tex]Slope(m) = \frac{8-5}{0-2} = -\frac{3}{2}[/tex]
y-intercept (b) = 8 (the line intercepts the y-axis at this point)
[tex]b = 8[/tex]
Substitute the value of m and b into [tex]y = mx + b[/tex]
Thus:
[tex]y = -\frac{3}{2}x + 8[/tex]
Therefore, the linear equation representing the graph in slope-intercept form is: [tex]y = -\frac{3}{2}x + 8[/tex]
Learn more about linear equations here:
https://brainly.com/question/16732089
