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Math  /  Algebra

Questiony=45x+3y=\frac{4}{5} x+3 y=3x+45y=3 x+\frac{4}{5} y=15x+45y=\frac{1}{5} x+\frac{4}{5} y=−45x+3y=-\frac{4}{5} x+3

Studdy Solution

STEP 1

1. The line passes through the points (−5,4)(-5, 4) and (3,0)(3, 0).
2. We need to determine which equation represents the line shown in the image.

STEP 2

1. Calculate the slope of the line using the given points.
2. Use the slope and one point to find the equation of the line in slope-intercept form.
3. Compare the derived equation with the given options to find the correct one.

STEP 3

Calculate the slope m m of the line using the formula: m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1} where (x1,y1)=(−5,4)(x_1, y_1) = (-5, 4) and (x2,y2)=(3,0)(x_2, y_2) = (3, 0).
m=0−43−(−5)=−43+5=−48=−12 m = \frac{0 - 4}{3 - (-5)} = \frac{-4}{3 + 5} = \frac{-4}{8} = -\frac{1}{2}

STEP 4

Use the slope −12-\frac{1}{2} and one of the points, say (3,0)(3, 0), to find the equation of the line in the form y=mx+by = mx + b.
Substitute the slope and the point into the equation: 0=−12(3)+b 0 = -\frac{1}{2}(3) + b
Solve for bb: 0=−32+b 0 = -\frac{3}{2} + b b=32 b = \frac{3}{2}
Thus, the equation of the line is: y=−12x+32 y = -\frac{1}{2}x + \frac{3}{2}

STEP 5

Compare the derived equation y=−12x+32 y = -\frac{1}{2}x + \frac{3}{2} with the given options.
None of the given options match the derived equation exactly. Therefore, it seems there might be an error in the problem statement or the options provided.
Since none of the options match the derived equation, there may be a mistake in the problem or the options provided. Please verify the options or the problem statement.

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