How do you write an equation in slope-intercept form of the line that passes through the points (-2, 6.9) and (-4, 4.6)?

Question

Isaiah Anthony · Accepted Answer

#y=1.15x+9.2# Since this is a linear variation of the form #y=mx+b#, any change in #x# will create a proportional change in #y#. #(-2)-(-4) = 2# and #(6.9)-(4.6) = 2.3 # so for every 2 changes in #x#, #y# changes by 2.3. Divide each side by 2, and 1 change in #x# corresponds to 1.15 in #y#, therefore the slope (#m#) must be 1.15. Now we have the equation #y=1.15x+b# Before, we said our change in #x# by 2 resulted in a change in #y# of 2.3. Therefore, if we move over right 2 from #(-2, 6.9)#, we reach the point #(0, 9.2)#. Since the #x#-value is 0, this is the y-intercept (#b#) The equation is #y=1.15x+9.2#

Nathan Axel · Answer

#color(blue)(y = 1.15 x + 9.2 " is the slope - intercept form"#

#color(green)(Slope = m = 1.15, "y-intercept " = 9.2# Equation of a line, knowing two points on it is given by #(y-y_1)/(y_2-y_1) = (x-x_1) / (x_2-x_1)# #(x_1,y_1) = -2, 6.9), (x_2,y_2) = (-4, 4.6)# #(y - 6.9) / (4.6 - 6.9) = (x +2) / (-4+2)# #(y - 6.9) / -2.3 = (x + 2) / -2# #(y - 6.9) = (2.3 * (x + 2))/2, " cross multiplying"# #y = 1.15 * (x + 2) + 6.9# #color(blue)(y = 1.15 x + 9.2 " is the slope - intercept form"# #color(green)(Slope = m = 1.15, "y-intercept " = 9.2#

Eva Abramson · Answer

undefined To write the equation of a line in slope-intercept form (y = mx + b) passing through two points (-2, 6.9) and (-4, 4.6), first find the slope (m) using the formula: $ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $. Then, substitute the slope and one of the points into the equation to solve for the y-intercept (b). Finally, write the equation in slope-intercept form.