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Svetllana [295]
2 years ago
14

What is an equation of the line that passes through the points (0,7) and (5,4? Put your answer in fully reduced form.

Mathematics
1 answer:
gregori [183]2 years ago
4 0

Answer <u>(assuming it can be in slope-intercept format)</u>:

y = -\frac{3}{5} x+7  

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 y = mx + b.

1) First, find the slope of the equation. Use the slope formula, m = \frac{y_2-y_1}{x_2-x_1}, to find the slope. Substitute the x and y values of the given points into the formula and simplify:

m = \frac{(4)-(7)}{(5)-(0)} \\m = \frac{4-7}{5-0} \\m = \frac{-3}{5}

Thus, the slope is -\frac{3}{5}.

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  y = mx + b. Substitute m and b for real values.

Since m represents the slope, substitute -\frac{3}{5}  in its place in the equation. Since b represents the y-intercept, substitute 7 in its place. This gives the following equation and answer:

y = -\frac{3}{5} x+7

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