How do you find the slope and intercept of #y = - x + 2#?

2 Answers
Apr 24, 2016

Answer:

Slope is #-1#, #y# intercept is #2#.

Explanation:

The equation of the graph is given in the form

#y=mx+b=-x+2#

where #m# is the gradient or slope, and #b# is the intercept on the #y# axis.

By simply comparing the two equations, we can see that #m=-1# and #b=2#.

This means the graph has a slope of #-1#, and crosses the #y# axis at point #(0,2)#.

Apr 24, 2016

Answer:

Gradient (slope) = -1
y-intercept#->(x,y)=(0,2)#
x-intercept#->(x,y)=(2,0#

Explanation:

Compare to #y=mx+c#

#m-> "gradient (slope)"#
# c -> "y-intercept"#

Given:#" "y=-x+2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine gradient")#

Write as:#" "y=[(-1)xx x]+2#

#color(blue)("The gradient "->m=-1#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine y-intercept")#

#color(blue)("y-intercept"->c=2#

#color(brown)("To prove y-intercept = 2")#

The graph crosses the y-axis at x=0. Substituting this value:

#color(brown)(y=-x+2" "->" "color(blue)(y=-(0)+2 = 2#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine x-intercept")#

The graph crosses the x-axis at y=0. Substituting this value

#" "0=-x+2#

Add #x# to both sides

#" "0+x=-x+x+2#

#color(blue)(" "x=0+2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~