The linear equation in slope-intercept form that the graph represents is [tex]y = 15x + 100[/tex]
The slope-intercept form of an equation is expressed as:
[tex]y = mx + b[/tex]
where,
m is the slope of the graph
b is the initial value or y-intercept
To find the linear equation, determine the values of the slope (m) and the y-intercept.
Slope (m) of the graph using two points on the line, [tex](0, 100)[/tex] and [tex](5, 175)[/tex]:
[tex]Slope=\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Let,
[tex](0,100) = (x_1, y_1)\\(5, 175) = (x_2, y_2)[/tex]
Plug on the values into the formula:
[tex]slope(m)= \frac{175 - 100}{5-0} \\= \frac{75}{5} \\Slope (m)= 15[/tex]
y-intercept (b) of the linear graph:
The y-intercept is the initial value or the point at which the line intercepts the y-axis.
The line intercepts the y-axis at [tex]y=100[/tex]
Therefore, y-intercept is 100
[tex]b = 100[/tex]
To write the linear equation in slope-intercept form, substitute [tex]m = 15[/tex] and [tex]b = 100[/tex] into [tex]y = mx + b[/tex]
Thus:
[tex]y = 15x + 100[/tex]
The linear equation that represents the graph in slope-intercept form is [tex]y = 15x + 100[/tex]
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