A line passes through the points (0, 9) and (9, 19). What is its equation in slope-intercept form?

Mathematics

1 answer:

STatiana [176]2 years ago

3 0

Answer:

y = 10/9x + 9

Step-by-step explanation:

To write the equation in its slope-intercept form, y = mx + b, we need to find the slope (m) of the line and its y-intercept (b).

Given the points (0, 9) and (9, 19), we can solve for the slope of the line using the following formula:

$m = \frac{y2 - y1}{x2 - x1}$

Let (x1, y1) = (0, 9)

and (x2, y2) = (9, 19)

Substitute these values on the formula:

$m = \frac{y2 - y1}{x2 - x1} = \frac{19 - 9}{9 - 0} = \frac{10}{9}$

Therefore, the slope (m ) = 10/9.

Next, the y-intercept is the point on the graph where it crosses the y-axis, and has the coordinates, (0, b ). It is also the value of the y when x = 0.

One of the given points is the y-intercept of the line, given by (0, 9). The y-coordinate, 9, is the value of b.

Therefore, the linear equation in slope-intercept form is: y = 10/9x + 9

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