Questions: Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (9,7) with x-intercept 5 Write an equation for the line in point-slope form. (Simplify your answer. Use integers or fractions for any numbers in the equation.)

$Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (9,7) with x-intercept 5 Write an equation for the line in point-slope form. (Simplify your answer. Use integers or fractions for any numbers in the equation.)$

Transcript text: Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through $(9,7)$ with $x$-intercept 5 Write an equation for the line in point-slope form. $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.)

Solution

Solution Steps

Step 1: Identify the Given Information

The given slope (m) is -1.75, and the point through which the line passes is (9, 7).

Step 2: Calculate the y-intercept (b) for the Slope-Intercept Form

To find the y-intercept $b$, we use the formula $b = y_1 - mx_1$. Substituting the given values, we get $b = 7 + 1.75 \times 9 = 22.75$.

Step 3: Write the Equation in Slope-Intercept Form

Substituting $m$ and $b$ into the slope-intercept form equation $y = mx + b$, we get: ^Slope-Intercept Form^: y = -1.75x + 22.75

Step 4: Write the Equation in Point-Slope Form

Using the given slope $m$ and the point $(9, 7)$, we directly substitute into the point-slope form equation $y - y_1 = m(x - x_1)$: ^Point-Slope Form^: y - 7 = -1.75(x - 9)