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Write an equation for a line passing through the point (7,5) that is parallel to y=(2)/(3)x+6 Then write a sec for a line passing through the given point that is perpendicular to the given line A slope-intercept equation for a line passing through the point (7,5) that is parallel to y=(2)/(3)x+6 is square (Simplify your answer. Type your answer in slope intercept form. Use integers or fractions for any numbers the equation.)

Pergunta

Write an equation for a line passing through the point (7,5) that is parallel to y=(2)/(3)x+6 Then write a sec
for a line passing through the given point that is perpendicular to the given line
A slope-intercept equation for a line passing through the point (7,5) that is parallel to y=(2)/(3)x+6 is square 
(Simplify your answer. Type your answer in slope intercept form. Use integers or fractions for any numbers
the equation.)

Write an equation for a line passing through the point (7,5) that is parallel to y=(2)/(3)x+6 Then write a sec for a line passing through the given point that is perpendicular to the given line A slope-intercept equation for a line passing through the point (7,5) that is parallel to y=(2)/(3)x+6 is square (Simplify your answer. Type your answer in slope intercept form. Use integers or fractions for any numbers the equation.)

Solução

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Beatriz MariaEspecialista · Tutor por 3 anos

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The equation of the line is \(y = \frac{2}{3}x + \frac{1}{3}\).

Explicação

## Step 1<br />The given line is \(y=\frac{2}{3}x+6\). The slope of this line is \(\frac{2}{3}\).<br /><br />## Step 2<br />A line parallel to another line has the same slope. Therefore, the slope of the line we are looking for is also \(\frac{2}{3}\).<br /><br />## Step 3<br />We know that the line we are looking for passes through the point (7,5). We can use the slope-intercept form of a line, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.<br /><br />## Step 4<br />Substitute the slope \(\frac{2}{3}\) and the point (7,5) into the equation \(y = mx + b\) to solve for \(b\).<br /><br />### \(5 = \frac{2}{3} * 7 + b\)<br /><br />## Step 5<br />Solve the equation for \(b\).<br /><br />### \(b = 5 - \frac{14}{3} = \frac{15}{3} - \frac{14}{3} = \frac{1}{3}\)<br /><br />## Step 6<br />Substitute the slope \(\frac{2}{3}\) and the y-intercept \(\frac{1}{3}\) into the slope-intercept form of a line to get the equation of the line.<br /><br />### \(y = \frac{2}{3}x + \frac{1}{3}\)
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