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Easy

Question

Write the equation in slope-intercept form of the line that passes through the points (-1, -5) and (4, -2).

hintHint:

The slope-intercept form of a line is y = mx + c, where m Is the slope of the line and c is the y- intercept. You obtain the value of y-intercept when you take x=0.
We are asked to find the equation of the line passing through the given points in the slope intercept form.

The correct answer is: y equals 3 over 5 x plus fraction numerator negative 22 over denominator 5 end fraction


    Step 1 of 2:
    The given points are: (-1,-5) and (4,-2). The slope intercept form equation is of the form, y = mx + c
    Now, the slope of the line is:
    m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
    m equals fraction numerator negative 2 minus left parenthesis negative 5 right parenthesis over denominator 4 minus left parenthesis negative 1 right parenthesis end fraction
    m equals fraction numerator negative 2 plus 5 over denominator 4 plus 1 end fraction
    m equals 3 over 5
    Thus, the equation of the line becomes; y equals 3 over 5 x plus c.
    Step 2 of 2:
    To get the value of the y-intercept, substitute any of the given points in the equation.
    y equals 3 over 5 x plus c
    negative 5 equals 3 over 5 left parenthesis negative 1 right parenthesis plus c
    negative 5 equals fraction numerator negative 3 over denominator 5 end fraction plus c
    negative 25 equals negative 3 plus 5 c
    negative 25 plus 3 equals 5 c
    negative 22 equals 5 c
    fraction numerator negative 22 over denominator 5 end fraction equals c
    Thus, the required equation of the line: y equals 3 over 5 x plus fraction numerator negative 22 over denominator 5 end fraction

    Let us assume the slope of the line to determine at a given point is also the y-intercept. You can utilize the slope-intercept formula, y = mx + b. (0, b). The y value of the y-intercept point is represented by the symbol 'b' in the formula. The slope of the line results when any two points on a line are entered into the slope formula. In this instance, 1/3 should be the response when 'P1' and 'P2' are put into the slope calculation. You can use two different versions of a line's general form to find a line's equation.
    The formula for equations of a line is:
    1) The formula for Point-Slope is (y - y1) = m (x – x1)
    2) The equation y = mx + b for the slope-intercept

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