CheerMath

Grade 8 Slope & Equations of Lines Practice

Find Slope and Use Slope-Intercept Form

Slope tells you how steep a line is and which way it leans. You'll measure it from a graph, from two points and from a table, then read a line's intercepts and write its equation.

Also known as Class 8 maths — the same topics, whether your school calls it grade, class or year.

Sign up for free

Sample questions

A few samples from this topic — try one, then show the answer.

  1. Recognize Positive, Negative, Zero and Undefined Slope

    What is the slope of the line through (0,  0)(0,\;0) and (5,  35)(5,\;35)?
    • 88{}
    • 77{}
    • 66{}
    • 3535{}
    Show answer
    Answer:
    77{}

  2. Identify Slope and y-Intercept and Write y = mx + b

    What are the slope kk {} and the yy{}-intercept cc {} of y  =  2x{y \; = \; 2x}?
    • k  =  −2k \; = \; -2, c  =  0c \; = \; 0
    • k  =  2k \; = \; 2, c  =  0c \; = \; 0
    • k  =  0k \; = \; 0, c  =  2c \; = \; 2
    • k  =  5k \; = \; 5, c  =  0c \; = \; 0
    Show answer
    Answer:
    k  =  2k \; = \; 2, c  =  0c \; = \; 0

  3. Connect Constant Rate of Change to Slope

    Compute the slope of the line through (0,  2)(0,\; 2) and (1,  6)(1,\; 6).give a numerical answer — a whole number, e.g., 3\quad {\scriptsize\color{gray}{\textrm{give a numerical answer — a whole number, e.g., 3}}}
    Show answer
    Answer:
    4

Want more like these? Try a round — no sign-up

A worked example

What is the slope of the line through (0,  0)(0,\;0) and (5,  35)(5,\;35)?
  1. Slope measures how steep a line is — how far it climbs or falls for each step it takes to the right.∙  \\ \bullet \;Steepness is a comparison between two points, so a single point can never give it; two are always needed.∙  \\ \bullet \;The two points given are (0,  0)(0,\;0) and (5,  35)(5,\;35).
  2. The two changes between those points have names: the vertical change is the rise\textit{rise} and the horizontal change is the run\textit{run}.∙  \\ \bullet \;Slope compares them as a rate, rise for each unit of run:\quadslope=riserun=y2−y1x2−x1∙  = \frac{\mathrm{rise}}{\mathrm{run}} = \frac{y_2 - y_1}{x_2 - x_1} \\ \bullet \;Subtract in the same order on the top and the bottom — second point minus first, both times — or the answer comes out with the wrong sign.
  3. Putting the two points into the formula:\\rise=35−0=35= 35 - 0 = 35 \\run=5−0=5= 5 - 0 = 5{}
  4. Now divide the rise by the run:\quadslope=355=7= \frac{35}{5} = 7 \\The rise divides evenly by the run, so the slope comes out as a whole number.
  5. The slope is 77{}.\quadSo the line climbs 77 {} units for every single unit it moves to the right, and the positive sign is what records that direction.
  6. Each of the other options comes from a specific slip, and it is worth seeing exactly where each one goes wrong:\\✘ 88{} — this is the kind of gap a single arithmetic slip leaves. Working the subtraction through carefully gives 355=7\frac{35}{5} = 7 \\✘ 66{} — this is the kind of gap a single arithmetic slip leaves. Working the subtraction through carefully gives 355=7\frac{35}{5} = 7 \\✘ 3535{} — this is the rise, the vertical change 3535{}. It is only half the job — the rise still has to be shared out over the run 55{}, and 355=7\frac{35}{5} = 7

More Grade 8 topics