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What is an equation of the line that passes through the point (-5,4) and is parallel to the line 3x 5y=35?

User Vikesh
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Final answer:

To find the equation of a line parallel to the line 3x + 5y = 35 and passing through the point (-5,4), use the point-slope form of a linear equation.

Step-by-step explanation:

To find the equation of a line parallel to the line 3x + 5y = 35, we need to determine the slope of the given line. We can rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Rearranging the equation, we have 5y = -3x + 35, and dividing by 5, we get y = -3/5x + 7.

The slope of this line is -3/5, so any line parallel to it will also have a slope of -3/5.

Since the line we want passes through the point (-5,4), we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Plugging in the values, we have y - 4 = -3/5(x - (-5)), simplifying further gives y - 4 = -3/5(x + 5).

Expanding, we get y - 4 = -3/5x - 3, and rearranging the equation, we obtain y = -3/5x + 1.

User Dgrat
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