How do you write the equation of a line in point slope form and slope intercept form given Point: (1, –7); Slope: -2/3?

Answer 1
Point-slope form is #y+7=-2/3(x-1)# .
y-intercept form is #y=-2/3x+ -19/3# .

Point-slope form.

Slope, #m#, = #-2/3#.
Point=#(1,-7)=x_1# and #y_1#.

Point-slope formula.

#y-y_1=m(x-x_1)# =
Substitute the values for #y_1# and #x_1# and #m#.
#y-(-7)=-2/3(x-1)# =
#y+7=-2/3(x-1)#

y-intercept form.

Slope, #m=-2/3#, #y=-7#, #x=1#.

y-intercept formula.

#y=mx+b# =
Substitute the values for #y#, #x#, and #m#. Solve for slope-intercept, #b#.
#-7=-2/3(1)+b# =
#-7=-2/3+b# =

Flip the equation (optional).

#b-2/3=-7# =

Add 2/3 to both sides.

#b=-7+2/3# =

Make the denominators the same.

#b= -7*3/3+2/3# =
#b=-21/3+2/3# =
#b=-19/3#

Now we can write the equation of the line in slope-intercept form.

#y=-2/3x+ -19/3#
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Answer 2

Point-slope form: ( y - y_1 = m(x - x_1) ) Given point ( (1, -7) ) and slope ( m = -\frac{2}{3} ), Point-slope form becomes: ( y - (-7) = -\frac{2}{3}(x - 1) )

Slope-intercept form: ( y = mx + b ) Given slope ( m = -\frac{2}{3} ) and point ( (1, -7) ), Substitute ( x = 1 ), ( y = -7 ), and ( m = -\frac{2}{3} ) into slope-intercept form to find ( b ): ( -7 = -\frac{2}{3}(1) + b ) ( -7 = -\frac{2}{3} + b ) ( b = -\frac{19}{3} )

Therefore, the equation in point-slope form is ( y + 7 = -\frac{2}{3}(x - 1) ), and in slope-intercept form is ( y = -\frac{2}{3}x - \frac{19}{3} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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