1 answer

How do you write an equation of a line given x-int of -4 and a y-int of 6?

Question:

How do you write an equation of a line given x-int of -4 and a y-int of 6?

Answers

#y = color(blue)(3/2)(x + color(red)(4))#

Or

#(y - color(red)(6)) = color(blue)(3/2)x#

Or

#y = color(blue)(3/2)x + 6#

Explanation:

x-intercept of -4 gives us the point (-4, 0)

y-intercept of 6 gives us the point (0. 6)

We can use the point-slope formula to write equations for this line.
The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the values from the points and calculating the slope gives:

#m = (color(red)(6) - color(blue)(0))/(color(red)(0) - color(blue)(-4))#

#m = (color(red)(6) - color(blue)(0))/(color(red)(0) + color(blue)(4)) = 6/4 = (2 xx 3)/(2 xx 2) = (color(red)(cancel(color(black)(2))) xx 3)/(color(red)(cancel(color(black)(2))) xx 2) = 3/2#

The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.

Substituting the slope we calculated and the first point gives:

#(y - color(red)(0)) = color(blue)(3/2)(x - color(red)(-4))#

#y = color(blue)(3/2)(x + color(red)(4))#

We can also substitute the slope we calculated and the second point giving:

#(y - color(red)(6)) = color(blue)(3/2)(x - color(red)(0))#

#(y - color(red)(6)) = color(blue)(3/2)x#

We can also solve this equation for #y# to give an equation in the slope-intercept form:

#y - color(red)(6) + 6 = color(blue)(3/2)x + 6#

#y - 0 = color(blue)(3/2)x + 6#

#y = color(blue)(3/2)x + 6#

.

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