Question

How can you write the equation for a linear function if you know only two ordered pairs for the function? These are the options; some may be used more than others.

Options: two ordered pairs, b, m, one set of ordered pairs

Use the two ordered pairs to find the slope, 1. . Then substitute 2. and 3. into y=mx+b to solve for 4. .

Answer 1

To find the x-intercept of the line with a slope of m and a y-intercept of (0, k), you can use the equation of a line in slope-intercept form: y = mx + b, where m is the slope, and b is the y-intercept.

You're given m = -3/7 and k = 18, so the equation of the line is:

y = (-3/7)x + 18

To find the x-intercept, set y to 0 and solve for x:

0 = (-3/7)x + 18

Now, isolate x:

(-3/7)x = -18

To solve for x, multiply both sides by -7/3:

x = (-7/3) * (-18)

x = 42

So, the x-intercept of the line is 42.

Explanation:

Answer 2

two ordered pairs, b, m, and one set of ordered pairs

Explanation:

To write the equation for a linear function if we know only two ordered pairs for the function, you can use the following steps:

Find the slope of the line. The slope of a line is calculated as follows:

`\boxed{\boxed{\sf slope = (y_2 - y_1)/(x_2 - x_1)}}`

Where (x1, y1) and (x2, y2) are two points on the line.

Substitute the slope and one of the ordered pairs into the equation
`\boxed{\boxed{\sf y = mx + b}}` to solve for the y-intercept.

Rewrite the equation in slope-intercept form, `
`\boxed{\boxed{\sf y = mx + b}}` .

Options:

a. two ordered pairs: This is required to find the slope of the line.

(b) is the y-intercept of the line, which is found by substituting the slope and one of the ordered pairs into the equation
`\boxed{\boxed{\sf y = mx + b}}` .

m: This is the slope of the line, which is calculated as follows:

`\boxed{\boxed{\sf slope = (y_2 - y_1)/(x_2 - x_1)}}`

Where (x1, y1) and (x2, y2) are two points on the line.

one set of ordered pairs: This is required to find the y-intercept of the line.

Therefore, the correct options to use to write the equation for a linear function if we know only two ordered pairs for the function are:

two ordered pairs, b, m, and one set of ordered pairs.