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Evgen [1.6K]
4 years ago
14

Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options.

Mathematics
1 answer:
vladimir1956 [14]4 years ago
7 0

Option A: y=\frac{3}{4}x+1 is the equation of the line.

Option E: y+2=\frac{3}{4}(x+4) is the equation of the line.

Explanation:

Given that the line is 3 x-4 y=7 and passes through the point (-4,-2)

We need to determine the equation of the line.

<u>Formula:</u>

The equation of the line can be determined using the formula,

y-y_1=m(x-x_1)

<u>Slope:</u>

Since, the lines are parallel, from the equation 3 x-4 y=7, we shall determine the slope.

Thus, we have,

-4 y=-3x+7

   y=\frac{3}{4} x+\frac{7}{4}

Thus, the slope of the equation is m=\frac{3}{4}

<u>Equation of line:</u>

Substituting m=\frac{3}{4} and the point (-4,-2) in the formula, we get,

y+2=\frac{3}{4}(x+4)

Hence, the equation of line is y+2=\frac{3}{4}(x+4)

Thus, Option E is the correct answer.

Let us write the equation of line y+2=\frac{3}{4}(x+4) in slope - intercept form.

Thus, we have,

y+2=\frac{3}{4}x+3

     y=\frac{3}{4}x+3-2

     y=\frac{3}{4}x+1

Thus, the equation of the line is y=\frac{3}{4}x+1

Hence, Option A is the correct answer.

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