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CA 2.2 Homework Score: 4/11 Answered: 4/11 square . < > Find the equation of the line through the point (3,-7) that is parallel to the line with equation y=-(3)/(10)x-3 The equation is square (Be sure to enter your answer as an equation) Progress saved

Pergunta

CA 2.2 Homework
Score: 4/11 Answered: 4/11
square 
. < >
Find the equation of the line through the point (3,-7) that is parallel to the line with equation
y=-(3)/(10)x-3
The equation is square  (Be sure to enter your answer as an equation)
Progress saved

CA 2.2 Homework Score: 4/11 Answered: 4/11 square . < > Find the equation of the line through the point (3,-7) that is parallel to the line with equation y=-(3)/(10)x-3 The equation is square (Be sure to enter your answer as an equation) Progress saved

Solução

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MathiasMestre · Tutor por 5 anos

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To find the equation of the line through the point $(3,-7)$ that is parallel to the line with equation $y=-\frac{3}{10}x-3$, we need to use the fact that parallel lines have the same slope.<br /><br />Step 1: Identify the slope of the given line.<br />The given line has the equation $y=-\frac{3}{10}x-3$. The slope of this line is $-\frac{3}{10}$.<br /><br />Step 2: Use the point-slope form of a linear equation.<br />The point-slope form of a linear equation is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.<br /><br />Step 3: Substitute the given point and slope into the point-slope form.<br />Substituting the point $(3,-7)$ and the slope $-\frac{3}{10}$ into the point-slope form, we get:<br />$y - (-7) = -\frac{3}{10}(x - 3)$<br /><br />Step 4: Simplify the equation.<br />Simplifying the equation, we have:<br />$y + 7 = -\frac{3}{10}(x - 3)$<br />$y + 7 = -\frac{3}{10}x + \frac{9}{10}$<br />$y = -\frac{3}{10}x + \frac{9}{10} - 7$<br />$y = -\frac{3}{10}x - \frac{61}{10}$<br /><br />Therefore, the equation of the line through the point $(3,-7)$ that is parallel to the line with equation $y=-\frac{3}{10}x-3$ is $y = -\frac{3}{10}x - \frac{61}{10}$.
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