A line with a slope of 2.5 passes through the point (3, 4) in the coordinate plane. What i… — ACT

A line with a slope of $2.5$ passes through the point $(3, 4)$ in the coordinate plane. What is the y-coordinate of the point on this line whose x-coordinate is $-1$ ?

Answer: -6

Answer

-6

By applying the slope formula

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

with the slope equal to

2.5

, the known point at

(3, 4)

, and the target point at

(-1, y)

, we obtain the linear equation

2.5 = \frac{y - 4}{-1 - 3}

. Simplifying the denominator gives

2.5 = \frac{y - 4}{-4}

. Multiplying both sides by

-4

yields

-10 = y - 4

. Finally, adding

4

to both sides gives

y = -6

Step-by-Step Solution

Set up the slope formula relation

2.5 = \frac{y - 4}{-1 - 3}

The slope

m

of a line passing through

(x_1, y_1)

and

(x_2, y_2)

is defined as the change in y-values divided by the change in x-values.

Solve for the unknown y-coordinate

y = -6

Simplifying the denominator to

-4

, multiplying both sides by

-4

gives

-10 = y - 4

, and adding

4

to both sides isolates

y

Key Concept

Finding a missing coordinate on a line given its slope and another coordinate point.

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