charginghypno23
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A line's slope is 5. The line passes through the point (5, 30). Find an equation for this line in both point-slope and slope-intercept form

A) An equation for this line in point-slope form is:

B) An equation for this line in slope-intercept form is.​

Sagot :

cosmickid287

Answer:

A) [tex]y-30=5(x-5)[/tex]

B) [tex]y = 5x + 5[/tex]  

Step-by-step explanation:

A) We know the slope and a point the line intersects. This means we have enough information to write the equation in point-slope form, or [tex]y-y_1 = m (x-x_1)[/tex]. Substitute values for the [tex]m[/tex], [tex]x_1[/tex] and [tex]y_1[/tex].

[tex]m[/tex] represents the slope, thus substitute 5 in its place in the equation. [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, thus use the x and y values of (5,30). Substitute 5 for [tex]x_1[/tex] and 30 for [tex]y_1[/tex]. This will give the following equation in point-slope form and one of the answers:

[tex]y-30=5(x-5)[/tex]

B) Now, to find the equation of the line in slope-intercept form, or [tex]y = mx + b[/tex]  format, isolate y in the point-slope form of the equation like below.

[tex]y -30=5(x-5)\\y -30 = 5x-25\\y =5x +5[/tex]

Thus, [tex]y = 5x + 5[/tex] is the slope-intercept form of the equation.

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