White an equation for a line passing through the point (2,5) that is parallel to y=(2)/(3)x+3 Then write a second equation for a line passing through the given point that is perpendicular to tho given line A slope-intercept equation for a line passing through the point (2,5) that is parallel to y=(2)/(3)x+3 (2)/(3) (Simplify your answer. Type your answer in slope intercept form. Use integers or fractions for any numbers in the equation.) Asecond slope-Intercept equation for a line passing through the point (2,5) that is perpendicular to the given line is -(3)/(2) (Simplify your answer. Type your answer in slope-Intercep tform Use integers or fractions for any numbers ln the equation.)

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$White an equation for a line passing through the point (2,5) that is parallel to y=(2)/(3)x+3 Then write a second equation for a line passing through the given point that is perpendicular to tho given line A slope-intercept equation for a line passing through the point (2,5) that is parallel to y=(2)/(3)x+3 (2)/(3) (Simplify your answer. Type your answer in slope intercept form. Use integers or fractions for any numbers in the equation.) Asecond slope-Intercept equation for a line passing through the point (2,5) that is perpendicular to the given line is -(3)/(2) (Simplify your answer. Type your answer in slope-Intercep tform Use integers or fractions for any numbers ln the equation.)$

White an equation for a line passing through the point (2,5) that is parallel to y=(2)/(3)x+3 Then write a second equation for a line passing through the given point that is perpendicular to tho given line A slope-intercept equation for a line passing through the point (2,5) that is parallel to y=(2)/(3)x+3 (2)/(3) (Simplify your answer. Type your answer in slope intercept form. Use integers or fractions for any numbers in the equation.) Asecond slope-Intercept equation for a line passing through the point (2,5) that is perpendicular to the given line is -(3)/(2) (Simplify your answer. Type your answer in slope-Intercep tform Use integers or fractions for any numbers ln the equation.)

Answer 1

The equation of the line parallel to the given line and passing through the point (2,5) is $y=\frac{2}{3}x+\frac{7}{3}$. The equation of the line perpendicular to the given line and passing through the point (2,5) is $y=-\frac{3}{2}x+\frac{11}{2}$.

Answer 2

## Step 1 The problem asks us to find two equations of lines that pass through the point (2,5). The first line is parallel to the given line $y=\frac{2}{3}x+3$, and the second line is perpendicular to the given line. ## Step 2 ### **The formula for the slope of a line is $m=\frac{y2-y1}{x2-x1}$** The slope of a line parallel to the given line is the same as the slope of the given line. Therefore, the slope of the parallel line is also $\frac{2}{3}$. ## Step 3 We can use the point-slope form of a line equation, $y-y1=m(x-x1)$, where $m$ is the slope and $(x1, y1)$ is a point on the line. Substituting the given point (2,5) and the slope $\frac{2}{3}$ into the equation, we get: $y-5=\frac{2}{3}(x-2)$ ## Step 4 Solving this equation for $y$ gives us the equation of the parallel line in slope-intercept form: $y=\frac{2}{3}x+\frac{7}{3}$ ## Step 5 The slope of a line perpendicular to the given line is the negative reciprocal of the slope of the given line. Therefore, the slope of the perpendicular line is $-\frac{3}{2}$. ## Step 6 Again using the point-slope form of a line equation, we substitute the given point (2,5) and the slope $-\frac{3}{2}$ into the equation, we get: $y-5=-\frac{3}{2}(x-2)$ ## Step 7 Solving this equation for $y$ gives us the equation of the perpendicular line in slope-intercept form: $y=-\frac{3}{2}x+\frac{11}{2}$

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