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Answer (assuming it can be in slope-intercept format):
[tex]y = -\frac{3}{5} x+7[/tex]
Step-by-step explanation:
When knowing the y-intercept of a line and its slope, we can write an equation representing it in slope-intercept form, or [tex]y = mx + b[/tex].
1) First, find the slope of the equation. Use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex], to find the slope. Substitute the x and y values of the given points into the formula and simplify:
[tex]m = \frac{(4)-(7)}{(5)-(0)} \\m = \frac{4-7}{5-0} \\m = \frac{-3}{5}[/tex]
Thus, the slope is [tex]-\frac{3}{5}[/tex].
2) Usually, we would have to use one of the given points and the slope to put the equation in point-slope form. However, notice that the point (0,7) has an x-value of 0. All points on the y-axis have an x-value of 0, thus (0,7) must be the y-intercept of the line. Now that we know the slope of the line and its y-intercept, we can already write the equation in slope-intercept format, represented by the equation [tex]y = mx + b[/tex]. Substitute [tex]m[/tex] and [tex]b[/tex] for real values.
Since [tex]m[/tex] represents the slope, substitute [tex]-\frac{3}{5}[/tex] in its place in the equation. Since [tex]b[/tex] represents the y-intercept, substitute 7 in its place. This gives the following equation and answer:
[tex]y = -\frac{3}{5} x+7[/tex]