These twenty-two problems practice Common Core standards F-IF.C.7a, F-LE.A.1a, F-LE.A.2 and A-CED.A.2. Find slopes from two points, switch between slope-intercept, point-slope and standard form, graph lines, and write equations of parallel and perpendicular lines.
The last six are word problems that ask for a linear model, a prediction and an interpretation. Work from easiest to hardest and check each equation with a point.
Problem 1: Slope from two points
Find the slope of the line through \((2,3)\) and \((6,11)\).
Problem 2: A negative slope
Find the slope of the line through \((-3,5)\) and \((1,-7)\).
Problem 3: A fractional slope
Find the slope of the line through \((-4,-1)\) and \((2,1)\). Write it as a fraction in simplest form.
Problem 4: Horizontal and vertical lines
Find the slope of each line, or write undefined.
- The line through \((2,5)\) and \((9,5)\)
- The line through \((3,-2)\) and \((3,6)\)
Problem 5: Read slope and intercept
The equation of a line is \(y=-\frac{3}{4}x+5\).
- State the slope and the y-intercept.
- Find \(y\) when \(x=8\).
Problem 6: Equation from a graph
Write the equation of the line shown in slope-intercept form.
Problem 7: Slope and a point
A line has slope \(\frac{4}{5}\) and passes through \((10,3)\). Write its equation in slope-intercept form.
Problem 8: Point-slope form
Write an equation in point-slope form for the line with slope 3 that passes through \((2,-1)\). Then rewrite it in slope-intercept form.
Problem 9: Line through two points
Write the equation of the line through \((1,3)\) and \((5,11)\) in slope-intercept form.
Problem 10: Standard to slope-intercept
Rewrite \(3x+4y=12\) in slope-intercept form and name the slope and y-intercept.
Problem 11: Slope-intercept to standard
Write \(y=-\frac{2}{5}x+4\) in standard form \(Ax+By=C\) with integer coefficients and \(A>0\).
Problem 12: Intercepts and graph
Find the x-intercept and y-intercept of \(4x-6y=24\), then graph the line.
Problem 13: Graph from slope-intercept
Graph \(y=-\frac{2}{3}x+1\).
Problem 14: Graph from point-slope
Graph the line \(y-2=\frac{1}{2}(x+3)\).
Problem 15: Parallel line
Write, in slope-intercept form, the equation of the line through \((3,-2)\) that is parallel to \(y=4x+1\).
Problem 16: Perpendicular line
Write the equation of the line through \((4,1)\) that is perpendicular to \(y=2x-5\).
Problem 17: Gym membership
A gym charges a one-time sign-up fee of $25 plus $18 per month. Let \(C\) be the total cost after \(m\) months.
- Write an equation for \(C\) in terms of \(m\).
- Find the cost after 9 months.
- After how many months has Maya paid a total of $277?
Problem 18: Data plan table
The table shows the monthly cost \(y\) in dollars of a data plan for \(x\) gigabytes.
- Show that the relationship is linear.
- Write an equation for \(y\).
- Find the cost for 15 gigabytes.
Problem 19: Road trip
On a road trip, Jamal’s car is 55 miles from his home after 1 hour and 145 miles from home after 3 hours. The car drives at a constant speed. Let \(d\) be the distance from home in miles after \(t\) hours.
- Find the speed of the car.
- Write an equation for \(d\).
- Find the distance after 5 hours.
Problem 20: Temperature conversion
Water freezes at \(0^{\circ}\text{C}\) (\(32^{\circ}\text{F}\)) and boils at \(100^{\circ}\text{C}\) (\(212^{\circ}\text{F}\)). Assume Fahrenheit temperature \(F\) is a linear function of Celsius temperature \(C\).
- Write an equation for \(F\) in terms of \(C\).
- Convert \(25^{\circ}\text{C}\) to Fahrenheit.
- Convert \(77^{\circ}\text{F}\) to Celsius.
Problem 21: Notebooks and binders
Sofia has $60 to spend at the school store. Notebooks cost $3 each and binders cost $5 each. The equation \(3x+5y=60\) describes the purchases that use all $60, where \(x\) is the number of notebooks and \(y\) is the number of binders.
- Find both intercepts and explain what each means.
- If Sofia buys 5 notebooks, how many binders can she buy?
Problem 22: Two savings plans
Priya has $20 saved and adds $8 each week. Ethan has $50 saved and adds $5 each week. Let \(w\) be the number of weeks and \(s\) the savings in dollars.
- Write an equation for each person.
- After how many weeks do they have the same amount, and how much is it?
See every chapter on the Algebra 1 math page.