2 answers

How do you graph the linear function #f(x)=-x+4#?

Question:

How do you graph the linear function #f(x)=-x+4#?

Answers

See a solution process below:

Explanation:

First, solve for two points which solve the function and plot these points:

First Point: For #x = 0#

#f(0) = -0 + 4#

#f(0) = 4# or #(0, 4)#

Second Point: For #x = 4#

#f(4) = -4 + 4#

#f(4) = 0# or #(4, 0)#

We can next plot the two points on the coordinate plane:

graph{(x^2+(y-4)^2-0.075)((x-4)^2+y^2-0.075)=0 [-20, 20, -10, 10]}

Now, we can draw a straight line through the two points to graph the line:

graph{(y+x-4)(x^2+(y-4)^2-0.075)((x-4)^2+y^2-0.075)=0 [-20, 20, -10, 10]}

.

#"see explanation"#

Explanation:

#"one way is to find the intercepts, that is where the graph"#
#"crosses the x and y axes"#

#• " let x = 0, in the equation for y-intercept"#

#• " let y = 0, in the equation for x-intercept"#

#x=0rArry=4larrcolor(red)"y-intercept"#

#y=0rArr-x+4=0rArrx=4larrcolor(red)"x-intercept"#

#"Plot the points "(0,4)" and "(4,0)#

#"Draw a straight line through them for graph"#
graph{(y+x-4)((x-0)^2+(y-4)^2-0.04)((x-4)^2+(y-0)^2-0.04)=0 [-10, 10, -5, 5]}

.

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