Question

A line passes through points (0, k) and (4,0) and has a slope of –2.5. Which statements are true regarding the graph of the line?

Answer 1

Answer:

A. The equation of the line is y=−2.5x+10.

C. The y-intercept is k.

F. The value of k is 10.

Step-by-step explanation:

A line passes through points (0, k) and (4,0) and has a slope of –2.5. Which statements are true regarding the graph of the line?

A. The equation of the line is y=−2.5x+10.

B. The equation of the line is y=−2.5x.

C. The y-intercept is k.

D. The y-intercept is 4.

E. The value of k is 4.

F. The value of k is 10.

Solution:

The slope of a line is the ratio of the vertical change to the horizontal change. The slope (m) of a line passing through $(x_1,y_1)\ and\ (x_2,y_2)$ is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Given that the line passes through (0, k) and (4,0)

$m=\frac{y_2-y_1}{x_2-x_1}$

$-2.5=\frac{0-k}{4-0}\\\\-2.5=\frac{-k}{4}\\\\k=10$

The equation of the line is given as:

$y-y_1=m(x-x_1)\\\\y-10=-2.5(x-0)\\\\y = -2.5x+10$

The y intercept is the value of y when x = 0, hence intercept = k

Answer 2

• The value of k is 10.

• From the coordinate given (0, 10) and (4, 0), we can see that the y intercept and x intercept of the graph is 10 and 4 respectively

Given the line that passes through points (0, k) and (4,0) and has a slope of –2.5, we need to get the value of "k

The formula for calculating the slope of a line is expressed as:

$m=\frac{y_2-y_1}{x_2-x_1}\\-2.5 = \frac{0-k}{4-0}\\-2.5=\frac{-k}{4} \\Cross \ multiply\\-2.5 \times 4 = -k\\-10 = -k\\k = 10$

Hence the value of k is 10.

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From the coordinate given (0, 10) and (4, 0), we can see that the y intercept and x intercept of the graph is 10 and 4 respectively