Line $s$ has an equation of $y = -\frac{7}{10}x - 1$ . Line $t$ , which is parallel to line $s$ , includes the point $(-6,5)$ . What is the equation of line $t$ ? $\newline$ Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Algebra 1

Write an equation for a parallel or perpendicular line

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Q. Line

s

has an equation of

y = -\frac{7}{10}x - 1

. Line

t

, which is parallel to line

s

, includes the point

(-6,5)

. What is the equation of line

t

\newline

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Find Slope of Line $s$ : Determine the slope of line $s$ . Line $s$ has an equation of $y = -\frac{7}{10}x - 1$ . The slope of a line in the form $y = mx + b$ is $m$ , where $m$ is the coefficient of $x$ . The slope of line $s$ is $-\frac{7}{10}$ .
Determine Slope of Line $t$ : Since line $t$ is parallel to line $s$ , it must have the same slope. Parallel lines have identical slopes. Therefore, the slope of line $t$ is also $-\frac{7}{10}$ .
Use Point-Slope Form: Use the point-slope form to find the equation of line $t$ . The point-slope form of a line is $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is a point on the line. We know the slope ( $m$ ) is $-\frac{7}{10}$ and the point $(x_1, y_1)$ is $(-6, 5)$ . Plugging these values into the point-slope form gives us $y - 5 = -\frac{7}{10}(x - (-6))$ .
Convert to Slope-Intercept Form: Simplify the equation from point-slope form to slope-intercept form. $\newline$ First, distribute the slope $-\frac{7}{10}$ across $(x + 6)$ . $\newline$ $y - 5 = -\frac{7}{10} \times x - (-\frac{7}{10} \times 6)$ $\newline$ $y - 5 = -\frac{7}{10} \times x + \frac{7}{10} \times 6$ $\newline$ Now, simplify $\frac{7}{10} \times 6$ . $\newline$ $\frac{7}{10} \times 6 = \frac{42}{10} = 4.2$ or $\frac{21}{5}$ in fraction form. $\newline$ So, $y - 5 = -\frac{7}{10} \times x + \frac{21}{5}$
Final Equation of Line t: Add $5$ to both sides of the equation to solve for $y$ . $\newline$ $y = -\frac{7}{10} \cdot x + \frac{21}{5} + 5$ $\newline$ Now, convert $5$ to a fraction with a denominator of $5$ to combine with $\frac{21}{5}$ . $\newline$ $5 = \frac{25}{5}$ $\newline$ So, $y = -\frac{7}{10} \cdot x + \frac{21}{5} + \frac{25}{5}$ $\newline$ Combine the fractions. $\newline$ $y = -\frac{7}{10} \cdot x + \frac{46}{5}$ $\newline$ This is the equation of line $t$ in slope-intercept form.