QuestionFebruary 2, 2026

A cyclist is competing in a 100-mile race. The cyclist travels at a speed of 17.5 miles per hour.Write an equation in point-slope form to show the relationship between x, the number of hours since the race started, and y, the cyclist's distance from the finish line. The equation in slope-intercept form is y=-17.5x+100 m=-17.5 nabla square . square Correct! Use 2 as x_(1) Substitute it into the equation to find y_(1)

A cyclist is competing in a 100-mile race. The cyclist travels at a speed of 17.5 miles per hour.Write an equation in point-slope form to show the relationship between x, the number of hours since the race started, and y, the cyclist's distance from the finish line. The equation in slope-intercept form is y=-17.5x+100 m=-17.5 nabla square . square Correct! Use 2 as x_(1) Substitute it into the equation to find y_(1)
A cyclist is competing in a 100-mile race. The cyclist travels at a speed of 17.5 miles per hour.Write an
equation in point-slope form to show the relationship between x, the number of hours since the race
started, and y, the cyclist's distance from the finish line.
The equation in slope-intercept form is y=-17.5x+100
m=-17.5 nabla 
square  .
square 
Correct!
Use 2 as x_(1) Substitute it into the equation to find y_(1)

Solution
4.0(292 votes)

Answer

The equation in point-slope form is y - 65 = -17.5(x - 2). Explanation 1. Identify the slope and initial point The slope of the line is given as m = -17.5, and the initial distance from the finish line is 100 miles when x = 0. This corresponds to the point (0, 100). 2. Use the given point (2, y_1) to find y_1 Substitute x_1 = 2 into the slope-intercept equation y = -17.5x + 100 to find y_1. \[ y_1 = -17.5(2) + 100 = -35 + 100 = 65 \] Thus, the point is (2, 65). 3. Write the equation in point-slope form Using the point-slope formula y - y_1 = m(x - x_1), substitute m = -17.5, x_1 = 2, and y_1 = 65: \[ y - 65 = -17.5(x - 2) \]

Explanation

1. Identify the slope and initial point<br /> The slope of the line is given as $m = -17.5$, and the initial distance from the finish line is $100$ miles when $x = 0$. This corresponds to the point $(0, 100)$.<br /><br />2. Use the given point $(2, y_1)$ to find $y_1$<br /> Substitute $x_1 = 2$ into the slope-intercept equation $y = -17.5x + 100$ to find $y_1$. <br />\[<br />y_1 = -17.5(2) + 100 = -35 + 100 = 65<br />\]<br />Thus, the point is $(2, 65)$.<br /><br />3. Write the equation in point-slope form<br /> Using the point-slope formula $y - y_1 = m(x - x_1)$, substitute $m = -17.5$, $x_1 = 2$, and $y_1 = 65$:<br />\[<br />y - 65 = -17.5(x - 2)<br />\]
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